Method and system for pre-coding for frequency selective radio communication channel

ABSTRACT

A method for processing signals to be transmitted in a MIMO system from a transmitter having at least two transmitting antennas to a receiver having at least two receiving antennas on a frequency selective communication channel. The method comprises estimating elements of a channel matrix H(q −1 ) based on time delays and complex valued coefficients associated with the communication channel to provide an estimated frequency variation function of each element of the channel matrix, and pre-coding the signals to be transmitted based on the estimated frequency variation function for each element. The invention also relates to a MIMO system; and a transmitter and a receiver for use in a MIMO system.

TECHNICAL FIELD

The present invention relates to a method for pre-coding incommunication systems over a frequency selective communication channelusing a system function approach, preferably used in a wirelesscommunication system. The invention also relates to a system.

BACKGROUND

An optimal transmission of several data streams, Multiple Input MultipleOutput (MIMO), is based on using antenna elements for which a pre-codingby a set of weights is used per stream. The pre-coding can be regardedas if each stream is subject to a beamformer, and where all streams aretransmitted simultaneously. The beamforming coefficients depend on theradio communication channel, because the optimal weights are theeigenvectors calculated by e.g. Singular Value Decomposition (SVD) ofthe channel matrix. A physical interpretation of the obtained weights isan antenna pattern. This antenna pattern describes how energy isradiated in directions which match the clusters that best transfer theenergy to a receiver.

In 3^(rd) Generation Partnership Project (3GPP), the concept ofpre-coding is used, as disclosed in 3GPP TS 36.211 (reference [1]). Inversion 1.1.1 of reference [1], the standard covers a primitive versionof pre-coding that contains a very limited number of distinct settings.These settings are described both using a one and a two antenna portscenario. The description in reference [1] is, from an antenna domainscenario, a method for creating beamforming coefficients for enumeratedsets.

The radio communication channel is often modelled as consisting ofclusters. These clusters are modelled as a collection of scatterers, andthe scattering is what mediates the radio wave. The channel depends onthe impact of clusters, for example, the number of objects and theirpositions. In the context of the present invention it is important torecognize that the impact of the clusters is a function of carrierfrequency. This means that the radio wave excites different physicalobjects depending of frequency. The channel perceived at, for example, amobile station will exhibit a frequency dependence which is related tothe clusters excited by the base station and vice versa. In the antennadomain, the frequency dependence has to be incorporated in a discussionon optimality.

In addition to the antenna domain, a radio communication link oftenfeatures an equalizer at the receiver side. The purpose of such a deviceis to mitigate the effect of Inter Symbol Interference (ISI) due to thechannel delay spread, e.g. the joint delay effect of propagation in thechannel. Typically, the equalizer does not discriminate on clustershaving the same delay but different spatial location. This implies thatthe equalizer can be viewed as operating in the temporal domain.

An observation which is of interest is that the pre-coding is describedby the standard in reference [1] with a code book approach. Thepre-coding is chosen as one out of a limited set of settings, such thatthe pre-coding coefficients are coarsely quantized in the spatialdomain. Here, the weights can be regarded as means to separate the datastreams at the receiver. In this context, the communication channel actsas a separation structure in a source separation problem (e.g. seereference [2]).

In US 2005/0101259 (reference [3]), by Tong et al., a method fortransmission signal processing is disclosed. Pre-coding signal weightsare determined based on CSI (channel state information) associated withseveral communication channels. Various techniques for determining CSIare disclosed including scattered pilot tones in OFDM systems. A matrixis used for pre-coding and an inverse matrix is used when decoding thereceived signals in the receiver. The described system handles a casewith no delays and a frequency flat channel, wherein no variations infrequency is allowed.

A drawback with the prior art is that pre-coding for a frequencyselective channel, i.e. a channel which is not flat, may not beaccomplished. A prior art concept to handle a frequency selectivechannel is based on a set of elements being complex matrices. Theseelements are weights to be used as pre-coding of an Orthogonal FrequencyDivision Multiple (OFDM) symbol. An OFDM symbol may be considered to bea collection of sub-carriers, e.g. the frequency bins of a DiscreteFourier Transform (DFT), see reference [4]. The idea is that the matrixoperates on a sub-carrier and its closest neighbours, with the rationalthat the channel is flat in this small interval. Obviously, the numberof matrices needed must be sufficiently many in order to describe thewhole channel.

In a Frequency Division Duplex (FDD) system, the channel is notreciprocal, therefore a feedback is needed. That is, if A istransmitting to B then B must inform A of the seen channel at B'sposition, and vice versa. Using a large number of matrices causes thefeedback to become significant. Hence, the bandwidth efficiencydecreases.

The number of matrices used to pre-code data may become quite large inorder to model a frequency selective channel. This makes the systemfeedback large which is undesired. Moreover, the number of possibleweights are few, when a code book based pre-coding is used, and thisresults in a poor match for an arbitrary channel.

SUMMARY OF THE INVENTION

An object with the present invention is to provide a method forpre-coding a frequency selective radio communication channel withimproved bandwidth efficiency compared to prior art solutions.

This object is achieved by a method for processing signals to betransmitted in a MIMO system. The MIMO system has, in it simplestconfiguration, a transmitter with at least two transmitting antennas anda receiver with at least two receiving antennas. More transmittingand/or receiving antennas may be provided in the MIMO system. Thesignals are transmitted from the transmitter to the receiver on afrequency selective communication channel, i.e. a non-flat channel. Achannel matrix, i.e. the channel transfer function, is estimated basedon measured time delays and complex valued coefficients in thecommunication channel in order to estimate functions describing thefrequency variation of the received signal in the receiver. The signalsto be transmitted is thereafter pre-coded (or pre-distorted) based onthe estimated functions to obtain a low inter stream interference and aknown symbol distortion (or even no symbol distortion).

An advantage with the present invention is that information regardingthe channel frequency variations is used to pre-code the transmittedsignals, whereby less information needs to be transmitted from thereceiver to the transmitter since the frequency variations may beexpressed as a mathematical expression needing less bandwidth.

Further objects and advantages may be found by a skilled person in theart from the detailed description.

BRIEF DESCRIPTION OF DRAWINGS

The invention will be described in connection with the followingdrawings that are provided as non-limited examples, in which:

FIG. 1 shows a first embodiment of the present invention in a TDDsystem.

FIG. 2 shows a flow chart illustrating the operation in a TDD systemaccording to FIG. 1.

FIG. 3 shows a first embodiment of the present invention in a FDDsystem.

FIG. 4 shows a flow chart illustrating the operation in a FDD systemaccording to FIG. 3.

FIGS. 5 a-5 c illustrate a preferred embodiment of estimating theelements of the channel matrix.

FIG. 6 shows an example of a pre-coding structure for a two antennacase.

FIG. 7 shows a flow diagram that illustrates a preferred embodiment of amethod according to the invention.

FIG. 8 shows an alternative flow diagram of the embodiment shown in FIG.7.

DETAILED DESCRIPTION

The general concept of the invention is to pre-distort a communicationsignal such that when it is received at a user receiver it has 1) a lowinter stream interference; 2) a known symbol distortion or no symboldistortion. The communication channel is modelled as a set of FiniteImpulse Response (FIR) filters instead of using the channel frequencygain function. These filters are used to pre-code the antenna signals(in time or frequency). In a Time Division Duplex (TDD) system, thecommunication channel might be reciprocal such that no feedback isneeded. However, sometimes it is beneficial to feedback the pre-codingcoefficients for TDD systems, e.g. if transmitter or receiver hardwarehas a large unknown impact on the channel. For a FDD system thesefilters are fed back to the transmitter, preferably truncated to two orthree coefficients. In the two antenna case, the communication channelmay be described by the following transfer function (or channel matrix):

$\begin{matrix}{{H\left( q^{- 1} \right)} = \begin{bmatrix}{H_{11}\left( q^{- 1} \right)} & {H_{12}\left( q^{- 1} \right)} \\{H_{21}\left( q^{- 1} \right)} & {H_{22}\left( q^{- 1} \right)}\end{bmatrix}} & (1)\end{matrix}$where q⁻¹ is the unit delay operator. The elements of the channel matrixH(q⁻¹) are FIR filters, which is a most realistic model for a radiocommunication channel.

Each FIR filter

${{H_{nm}\left( q^{- 1} \right)} = {\sum\limits_{k = L_{\min}}^{L_{\max}}{h_{k,{nm}}q^{- k}}}},$where h_(k,nm) is a complex valued coefficients for element nm and q⁻krepresents time delays. The summation limits L_(min), L_(max) arepreferably selected by model order selection methods, e.g Aikake, seereference [5].

FIG. 1 shows a first embodiment of the present invention in a TDD system(i.e. when no feedback required). The MIMO system 10 comprises a firsttransceiver 1 having two antennas 11 and 12, and a second transceiver 2having two antennas 13 and 14. The transceiver 1 is provided with apilot signal generator 15 that transmits pilot signals to thetransceiver 2 using the antennas 11 and 12. The pilot signals arereceived at the antennas 13 and 14 of the transceiver 2 and elements ina 2 by 2 channel matrix for the communication channel are estimated inthe estimator 16 based on delays associated with the communicationchannel to provide an estimated frequency variation function of eachelement of the channel matrix. A calculator unit 17 in the transceiver 2is used to calculate a 2 by 2 pre-coding matrix based on the estimatedfrequency variation function for each element of the channel matrix inorder to pre-code the signals to be transmitted in a pre-coder 18. Thefunction of the calculator unit 17 is described in more detail below,and the pre-coder is preferably implemented as FIR filters. Data streamsx₁(n) and x₂(n) are fed to the transceiver 2 and pre-coded in thepre-coder 18 before the pre-coded signals are transmitted from theantennas 13 and 14 of the transceiver 2. These signals are thereafterreceived at the antennas 11 and 12 of the transceiver 1 and filtered inan optional filter 19 before estimated data streams {circumflex over(x)}₁(n) and {circumflex over (x)}₂(n) are outputted from thetransceiver 1 for further processing.

It should be noted that the transceiver 1 is also equipped with anestimator, calculator unit and pre-coder for transmitting data to thetransceiver 2, which is also equipped with a pilot generator to transmitpilot signals to the transceiver 1 and optionally a filter to be able toreceive data signals from the transceiver 1. These are omitted from thedrawing for the sake of clarity.

FIG. 2 shows a flow chart illustrating the operation in a TDD systemaccording to FIG. 1. The flow starts at step 20, and pilot signals aretransmitted from a first transceiver (e.g. transceiver 1) in step 21.The pilot signals are received at a second transceiver (e.g. transceiver2) and the elements of the channel matrix are estimated in step 22 toprovide an estimated frequency variation function of each element of thechannel matrix. A pre-coding matrix is calculated at step 23, and datastreams x₁(n) and x₂(n) intended to be transmitted from the secondtransceiver 2 are pre-coded based on the estimated frequency variationfunction for each element in the channel matrix at step 24. Signalsz₁(n) and z₂(n) are received at the first transceiver 1 and are filteredat step 25 to output estimated data streams {circumflex over (x)}₁(n)and {circumflex over (x)}₂(n) from the first transceiver 1 for furtherprocessing. The flow ends at step 26. It should be noted that step 25 isoptional, see below.

FIG. 3 shows a second embodiment of the present invention in a FDDsystem (feedback required). The MIMO system 28 comprises a transmitter 3having three antennas 29, 30 and 31, and a receiver 4 having threeantennas 32, 33 and 34. The transmitter 3 is provided with a pilotsignal generator 35 that transmits pilot signals to the receiver 4 usingthe antennas 29-31. The pilot signals are received at the antennas 32-34of the receiver 4 and elements in a 3 by 3 channel matrix for thecommunication channel are estimated in the estimator 36 based on delaysassociated with the communication channel to provide an estimatedfrequency variation function of each element of the channel matrix.Information regarding the estimated frequency variation functions istransferred from the receiver 4 to the transmitter 3. A calculator unit37 in the transmitter 3 is used to calculate a 3 by 3 pre-coding matrixbased on the estimated frequency variation function for each element ofthe channel matrix in order to pre-code the signals to be transmitted ina pre-coder 38. The function of the calculator unit 37 is described inmore detail below, and the pre-coder is preferably implemented as FIRfilters. Alternatively, the pre-coding matrix is calculated in thereceiver based on delays associated with the communication channel, andthis pre-coding matrix is then transferred to the transmitter, i.e. from4 to 3. Data streams x₁(n), x₂(n) and x₃(n) are fed to the transmitter 3and pre-coded in the pre-coder 38 before the pre-coded signals aretransmitted from the antennas 29-31 of the receiver 4 over acommunication channel. These signals are thereafter received at theantennas 32-34 of the transmitter A and filtered in an optional filter39 before estimated data streams {circumflex over (x)}₁(n), {circumflexover (x)}₂(n) and {circumflex over (x)}₃(n) are outputted from thereceiver 4 for further processing.

FIG. 4 shows a flow chart illustrating the operation in a FDD systemaccording to FIG. 3. The flow starts at step 40, and pilot signals aretransmitted from a transmitter 3 in step 41. The pilot signals arereceived at a receiver 4 and the elements of a 3×3 channel matrix areestimated in step 42 to provide an estimated frequency variationfunction of each element of the channel matrix. Information regardingthe estimated frequency variation functions is transferred from thereceiver 4 to the transmitter 3 in step 43, and a 3×3 pre-coding matrixis calculated in step 44, and data streams x₁(n), x₂(n) and x₃(n)intended to be transmitted from the transmitter 3 are pre-coded based onthe estimated frequency variation function for each element in thechannel matrix at step 45. Signals z₁(n), z₂(n) and z₃(n) are receivedat the receiver 4 and are filtered at step 46 to output estimated datastreams {circumflex over (x)}₁(n), {circumflex over (x)}₂(n) and{circumflex over (x)}₃(n) from the receiver 4 for further processing.The flow ends at step 47. It should be noted that step 46 is optional,see below.

In the embodiments described above, the same number of antennas at bothtransmitter and receiver are selected. The reason for doing this is thatthe number of data streams that may be transferred between thetransmitter and the receiver in limited to the minimum number ofantennas at both the transmitter and the receiver, i.e. min (N, M),where N is the number of transmitting antennas and M is the number ofreceiving antennas.

It should be noted that the pre-coding matrix W(q⁻¹) may be calculatedin the receiver and thereafter transferred to the transmitter topre-code the signals to be transmitted.

FIGS. 5 a-5 c illustrate a preferred embodiment for estimating theelements of the channel matrix. A transmitter 5 sends pilot signalswhich a receiver 6 uses to estimate the channel model in the receiver 6,as illustrated in FIG. 5 a. This channel model is a N by M matrix withFIR filters as elements, where N is the number of transmitting antennasand M is the number of receiving antennas. The matrix elements arequantized such that each element being expressed as a polynomial,containing a few coefficients. The number of coefficients to betransmitted can, for example, be determined by model order selectionmethods, e.g. Aikake Information Criterion (AIC) (see reference [5]).The polynomials are transmitted from 6 to 5 as illustrated in FIG. 5 b.Now the transmitter 5 knows what channel the receiver 6 experiences.Based on these polynomials a pre-coding matrix is calculated and used topre-code the data transmitted from 5 as illustrated in FIG. 5 c. Thepre-coding can take place in the time domain or in the frequency domain.A polynomial representation is a parametric representation of thefrequency domain. A clear advantage is that instead of having severalpiecewise constant weights, a continuous function defining the properpre-coding is obtained.

FIG. 6 shows one proposed pre-coding structure for the two antenna case.Two independent data streams x₁(n) and x₂(n) are fed into the pre-codingstructure 60, and two transmit signals y₁(n) and y₂(n) are fed to arespective transmitting antenna 61, 62. Four FIR filters 63-66 and twosummation circuits 67 and 68 are arranged within the pre-codingstructure 60. A first data stream x₁(n) is connected to a first FIRfilter 63 and a second FIR filter 64, and a second data stream x₂(n) isconnected to a third FIR filter 65 and a fourth FIR filter 66. Each FIRfilter is configured to provide a proper pre-coding of the data streamsx₁(n) and x₂(n) together with the summation circuits 67 and 68. Theoutputs of the first and third FIR-filter are connected to a firstsummation circuit 67 to produce the first transmit signal y₁(n), and theoutputs of the second and fourth FIR filter are connected to a secondsummation circuit 68 to produce the second transmit signal y₂(n).

The FIR filter may be configured based on the channel matrix estimate oron eigenvector functions as illustrated below.

Pre-Coding Based on Channel Estimates

An inverse of the channel matrix may be used to pre-code the datastreams before they are transmitted. The FIR representation in FIG. 6results in the following matrix representation

-   first FIR filter (63): W₁₁(q⁻¹)-   second FIR filter (64): W₂₁(q⁻¹)-   third FIR filter (65): W₁₂(q⁻¹)-   fourth FIR filter (66): W22(q⁻¹)

Each FIR filter

${{W_{nm}\left( q^{- 1} \right)} = {\sum\limits_{k = K_{\min}}^{K_{\max}}{a_{k,{nm}}q^{- k}}}},$where α_(k,nm) is a complex valued coefficients for element nm andq^(−k) represents time delays. The interval K_(min),K_(max) ispreferably selected to be a sub-set of the interval L_(min), L_(max).

$\begin{matrix}{{W\left( q^{- 1} \right)} = \begin{bmatrix}{W_{11}\left( q^{- 1} \right)} & {W_{12}\left( q^{- 1} \right)} \\{W_{21}\left( q^{- 1} \right)} & {W_{22}\left( q^{- 1} \right)}\end{bmatrix}} & (2)\end{matrix}$

Multiplying Eq. (1) and Eq. (2) yields the matrix

$\begin{matrix}{{P\left( q^{- 1} \right)} = {\quad\begin{bmatrix}{{{W_{11}\left( q^{- 1} \right)}{H_{11}\left( q^{- 1} \right)}} + {{W_{21}\left( q^{- 1} \right)}{H_{12}\left( q^{- 1} \right)}}} & {{{H_{11}\left( q^{- 1} \right)}{W_{12}\left( q^{- 1} \right)}} + {{H_{12}\left( q^{- 1} \right)}{W_{22}\left( q^{- 1} \right)}}} \\{{{H_{21}\left( q^{- 1} \right)}{W_{11}\left( q^{- 1} \right)}} + {{H_{22}\left( q^{- 1} \right)}{W_{21}\left( q^{- 1} \right)}}} & {{{H_{21}\left( q^{- 1} \right)}{W_{12}\left( q^{- 1} \right)}} + {{H_{22}\left( q^{- 1} \right)}{W_{22}\left( q^{- 1} \right)}}}\end{bmatrix}}} & (3)\end{matrix}$

Selecting the pre-coding filters according to:W ₁₁(q ⁻¹)=H ₂₂(q ⁻¹),W ₂₂(q ⁻¹)=H ₁₁(q ⁻¹),W ₁₂(q ⁻¹)=−H ₁₂(q ⁻¹), andW ₂₁(q ⁻¹)=−H ₂₁(q ⁻¹)results in a diagonal matrix P(q⁻¹) with det(H(q⁻¹)) on the diagonal.Evidently, the two data streams are separated, but filtered bydet(H(q⁻¹)), which is a minor issue since that filter is known. In fact,the filter can also be avoided by pre-filtering the data streams by(det(H(q⁻¹)))⁻¹, either in the transmitter before being transmitted tothe receiver, or in a filter in the receiver before the signal isdecoded. The selection corresponds to the inverse of Eq. (1) which israther natural. This also means that the result is general for anynumber of antennas. That is, the elements of the pre-coding matrixshould be chosen as the channel matrix determinant times the cofactorsof the inverse of the channel matrix.

FIG. 7 shows a flow diagram that illustrates a preferred embodiment of amethod according to the invention based on the inverse calculation ofthe channel matrix to obtain the pre-coding matrix.

Pilot signals are generated and transmitted from the transmitter to thereceiver. The channel matrix estimate is calculated based on thereceived pilot signals in the receiver, and polynomials are prunedaccording to some penalty function, e.g. AIC. The polynomials arethereafter transmitted to the transmitter, and an inverse of the channelmatrix is computed in terms of cofactors. The spectral gain for eachsub-carrier in an OFDM system is computed using the parametric model inthe transmitter, and the gains are applied to the data (pre-coding) andthe pre-coded data are thereafter transmitted to the receiver. Thereceived data is distorted by (det(H(q⁻¹)))⁻¹, i.e. one over thechannel-matrix determinant, and may thereafter be decoded.

FIG. 8 shows an alternative flow diagram in which all steps includingthe pre-coding step is performed as illustrated in FIG. 7. Filtering by(det(H(q⁻¹)))⁻¹, i.e. one over the channel matrix determinant isperformed, in the transmitter before transmitting the pre-coded data tothe receiver. In that case, the received data may be decoded without anyadditional filtering.

The polynomials represent the frequency variation functions upon whichthe pre-coding matrix is calculated. However, it is preferred that alimited number of coefficients, e.g. 3-4, in the polynomials aretransmitted from the receiver to the transmitter in order to minimizethe bandwidth needed to transfer information regarding the frequencyvariation functions. The channel matrix needs to be estimated at regularintervals to monitor changes in the communication channel, especially inthe case where the transmitter and/or receiver is a mobile station andnot part of the stationary communication network, see FIG. 5 a-5 c.

Pre-Coding Based on Eigenvector Functions

In the prior art, it was mentioned that the optimal weights are thoserelated to the eigenvectors of the channel matrix. Typically, this isdescribed and derived for a flat channel, but in the present inventionthe concept is extended to frequency selective channels.

The communication channel, for the two antenna case, is given by Eq.(1), and Eigen value functions can be calculated by evaluating:|H(q ⁻¹)−λ(q ⁻¹)I|=0,   (4)

Where the Eigen value functions becomes

$\begin{matrix}{{\lambda\left( q^{- 1} \right)} = {\frac{{H_{11}\left( q^{- 1} \right)} + {H_{22}\left( q^{- 1} \right)}}{2} \pm \sqrt{\left( \frac{{H_{11}\left( q^{- 1} \right)} - {H_{22}\left( q^{- 1} \right)}}{2} \right)^{2} + {{H_{12}\left( q^{- 1} \right)}{H_{21}\left( q^{- 1} \right)}}}}} & (5)\end{matrix}$

The eigenvector function v(q⁻¹) can be found from the followingexpression:H(q ⁻¹)v(q ⁻¹)=λ(q ⁻¹)v(q ⁻¹)   (6)

The two antenna case evaluates for example to:

$\begin{matrix}{{v_{1}\left( q^{- 1} \right)} = {\begin{bmatrix}{v_{11}\left( q^{- 1} \right)} \\{v_{12}\left( q^{- 1} \right)}\end{bmatrix} = {\quad\left\lbrack {{- \frac{{H_{11}\left( q^{- 1} \right)} - {H_{22}\left( q^{- 1} \right)}}{2}} + \left. \quad\overset{H_{12}{(q^{- 1})}}{\sqrt{\left( \frac{{H_{11}\left( q^{- 1} \right)} - {H_{22}\left( q^{- 1} \right)}}{2} \right)^{2} + {{H_{12}\left( q^{- 1} \right)}{H_{21}\left( q^{- 1} \right)}}}} \right\rbrack} \right.}}} & (7) \\{and} & \; \\{{v_{2}\left( q^{- 1} \right)} = {\begin{bmatrix}{v_{21}\left( q^{- 1} \right)} \\{v_{22}\left( q^{- 1} \right)}\end{bmatrix} = {\quad{\quad{\quad{\quad{\quad\left\lbrack {{- \frac{{H_{11}\left( q^{- 1} \right)} - {H_{22}\left( q^{- 1} \right)}}{2}} + \overset{H_{12}{(q^{- 1})}}{{\quad\quad}{\quad{\quad{\quad{\quad\sqrt{\left( \frac{{H_{11}\left( q^{- 1} \right)} - {H_{22}\left( q^{- 1} \right)}}{2} \right)^{2} + {{H_{12}\left( q^{- 1} \right)}{H_{21}\left( q^{- 1} \right)}}}}}}}}} \right\rbrack}}}}}}} & (8)\end{matrix}$

Equations (7) and (8) can be transformed into a frequency domainrepresentation simply by substituting q^(k)=e^(jωk), where ω isfrequency. Obviously, a frequency representation can for example be usedto optimally weight an OFDM symbol.

It is an advantage that a typical channel can be modelled with a fewtime delays and complex valued coefficients. Hence, instead oftransmitting a large amount of frequency weights, a time domain model istransmitted. This model may, at the receiver, be used in the time orfrequency domain. The point is that a large reduction in amount ofrequired feedback can be made.

The calculator unit 17 and 37, previously described in connection withFIGS. 1 and 3, are configured to calculate the pre-coding matrix W(q⁻¹)based on the estimated frequency variation function for each element ofthe channel matrix H(q⁻¹), i.e. based on the inverse of the channelmatrix or eigenvector functions of the channel matrix, in order topre-code the signals to be transmitted.

Abbreviations

3GGP 3^(rd) Generation Partnership Project

AIC Akaike Information Criterion

DTF Discrete Fourier Transform

FDD Frequency Division Duplex

FIR Finite Impulse Response

ISI Inter Symbol Interference

LTE Long Term Evolution

MIMO Multiple Input Multiple Output

OFDM Orthogonal Frequency Division Multiplex

SVD Singular Value Decomposition

TDD Time Division Duplex

REFERENCES

-   [1] 3^(rd) Generation Partnership Project, 650 Route des Lucioles,    Sophia Antipolis, Valbonne FRANCE, “Technical Specification Group    Radio Access Network; Physical Channels and Modulation”; 3GGP TS    36.211, v1.1.1 edition, 2007.-   [2] U. Lindgren and H. Broman. “Source separation: Using a criterion    based on second order statistics”, IEEE Trans. on Signal Processing,    46(7), July 1998.-   [3] US 2005/0101259, Tong et al. “Communication channel optimization    systems and methods in multi-user communication systems”, May 12,    2005.-   [4] H. Schulze and C. Lüders. “Theory and applications of OFDM and    CDMA wideband wireless communications”, John Wiley 85 Sons Inc.,    Chichester, West Sussex PO19 8SQ, England, 2005.-   [5] P. Stocia and Y Selen. Model-order selection a review of    information criterion rules. IEEE Signal Processing Magazine, pages    36-47, July 2004.

The invention claimed is:
 1. A method for processing signals to betransmitted in a Multiple Input Multiple Output (MIMO) system from atransmitter having at least two transmitting antennas to a receiverhaving at least two receiving antennas on a frequency selectivecommunication channel, comprising the steps of: estimating elements of achannel matrix H(q⁻¹) in the receiver based on time delays and complexvalued coefficients associated with the communication channel to providean estimated frequency variation function of each element of the channelmatrix H(q⁻¹); transferring the estimated frequency variation functionfrom the receiver to the transmitter; and pre-coding the signals to betransmitted based on the estimated frequency variation function for eachelement of the channel matrix H(q⁻¹).
 2. The method according to claim1, wherein the method further comprises the step of calculating apre-coding matrix W(q⁻¹) based on the estimated frequency variationfunction for each element of the channel matrix H(q⁻¹) to pre-code thesignals to be transmitted.
 3. The method according to claim 2, furthercomprising the step of implementing the pre-coding matrix W(q⁻¹) asFinite Impulse Response (FIR) filters in the transmitter.
 4. The methodaccording to claim 2, wherein the elements of the channel matrix H(q⁻¹)are estimated by: transmitting pilot signals from the transmitter to thereceiver; estimating the elements of the channel matrix H(q⁻¹) in thereceiver based on the pilot signals; quantizing each element of thechannel matrix H(q⁻¹) to obtain a polynomial having a predeterminednumber of coefficients representing each estimated frequency variationfunction; and using the polynomials to calculate the pre-coding matrixW(q⁻¹).
 5. The method according to claim 2, wherein the pre-codingmatrix W(q⁻¹) represents an inverse of the channel matrix H(q⁻¹).
 6. Themethod according to claim 2, wherein the pre-coding matrix W(q⁻¹)represents eigenvector functions of the channel matrix H(q⁻¹).
 7. Themethod according to claim 1, wherein the MIMO system is an OrthogonalFrequency Division Multiplexing (OFDM) system.
 8. The method accordingto claim 1, further comprising pre-coding in the time domain or in thefrequency domain.
 9. A Multiple Input Multiple Output (MIMO) systemhaving a transmitter having at least two transmitting antennas and areceiver having at least two receiving antennas, the MIMO system beingconfigured to process signals to be transmitted from the transmitter tothe receiver on a frequency selective communication channel, the MIMOsystem comprising: an estimator in the receiver configured to estimateelements in a channel matrix H(q⁻¹) based on time delays and complexvalued coefficients associated with the communication channel to providean estimated frequency variation function of each element of the channelmatrix H(q⁻¹); means to transfer the estimated frequency variationfunction from the receiver to the transmitter; and a pre-coderconfigured to pre-code the signals to be transmitted based on theestimated frequency variation function for each element of the channelmatrix H(q⁻¹).
 10. The MIMO system according to claim 9, wherein theMIMO system is provided with a calculator unit configured to calculate apre-coding matrix W(q⁻¹) based on the estimated frequency variationfunction for each element of the channel matrix H(q⁻¹) to pre-code thesignals to be transmitted.
 11. The MIMO system according to claim 10,wherein the pre-coder is implemented as Finite Impulse Response (FIR)filters representing the pre-coding matrix W(q⁻¹).
 12. The MIMO systemaccording to claim 10, wherein the transmitter is configured to transmitpilot signals to the receiver and the estimator of the receiver isconfigured to estimate the elements of the channel matrix H(q⁻¹) basedon the pilot signals, and quantize each element of the channel matrixH(q⁻¹) to obtain a polynomial having a predetermined number ofcoefficients representing each estimated frequency variation function,the polynomials being used in the calculator unit of the transmitter tocalculate the pre-coding matrix W(q⁻¹).
 13. The MIMO system according toclaim 10, wherein the calculator unit is configured to calculate thepre-coding matrix W(q⁻¹) as an inverse of the channel matrix H(q⁻¹). 14.The MIMO system according to claim 10, wherein the calculator unit isconfigured to calculate the pre-coding matrix W(q⁻¹) based oneigenvector functions of the channel matrix H(q⁻¹).
 15. The MIMO systemaccording to claim 9, wherein the MIMO system is an Orthogonal FrequencyDivision Multiplexing (OFDM) system.
 16. The MIMO system according toclaim 9, wherein the pre-coder operates in the time domain or thefrequency domain.
 17. A transmitter configured to communicate with areceiver in a Multiple Input Multiple Output (MIMO) system on afrequency selective communication channel, the transmitter having atleast two transmitting antennas and configured to process signals to betransmitted to the receiver, the transmitter comprising: a pre-coderconfigured to pre-code the signals to be transmitted based on anestimated frequency variation function for each element in a channelmatrix H(q⁻¹) estimated in and received from the receiver.
 18. Thetransmitter according to claim 17, wherein the transmitter furthercomprises a calculator unit configured to calculate a pre-coding matrixW(q⁻¹) based on the estimated frequency variation function for eachelement of the channel matrix H(q⁻¹) to pre-code the signals to betransmitted.
 19. The transmitter according to claim 18, wherein thepre-coder is implemented as Finite Impulse Response (FIR) filtersrepresenting the pre-coding matrix W(q⁻¹).
 20. The transmitter accordingto claim 18, wherein the calculator unit is configured to calculate thepre-coding matrix W(q⁻¹) as an inverse of the channel matrix H(q⁻¹), oreigenvector functions of the channel matrix H(q⁻¹).
 21. A receiverconfigured to communicate with a transmitter in a Multiple InputMultiple Output (MIMO) system on a frequency selective communicationchannel, the receiver having at least two receiving antennas, thereceiver comprising an estimator configured to estimate elements in achannel matrix H(q⁻¹) based on time delays and complex valuedcoefficients associated with the communication channel to provide anestimated frequency variation function of each element of the channelmatrix H(q⁻¹) and means to communicate the estimated frequency variationfunction to the transmitter.
 22. The receiver according to claim 21,wherein the receiver further comprises means to receive pilot signalsfrom the transmitter, and the estimator of the receiver is configured toestimate the elements of the channel matrix H(q⁻¹) based on the pilotsignals; and quantize each element of the channel matrix H(q⁻¹) toobtain a polynomial having a predetermined number of coefficientsrepresenting each estimated frequency variation function, thepolynomials are communicated to the transmitter.